Talk:General relativity/Archive 12

The introduction to the "evolution equations" section seems rather odd to me:

:Each solution of Einstein's equation encompasses the whole history of a universe—it is not just some snapshot of how things are, but a whole, possibly matter-filled, spacetime. It describes the state of matter and geometry everywhere and at every moment in that particular universe.

What exactly is the distinction being made here?

Surely the "solution" of an evolution equation is equally the whole history of the system it describes, exactly analogously.

Is this section in fact talking about boundary conditions? Is it saying that it is not immediately obvious that the description of the universe can be mapped forward from a complete description on an initial space-like surface?

Or is the point that there are restrictions, and not any such initial configuration is possible?

I'm not clear about the distinction the section is trying to draw. -- Jheald (talk) 12:34, 25 November 2008 (UTC)

:My impression is that it is simply making the point for the non-technical reader that a single solution describes spacetime not a spatial configuration at a single instant (as might be imagined by the reader) in time. Martin Hogbin (talk) 11:47, 17 July 2009 (UTC)

In 1965, Steven Weinberg published the paper "Photons and gravitons in perturbation theory: Derivation of Maxwell's and Einstein's Equations" Physical Review B 138, 988 - 1002 .

This is what Misner, Thorne and Wheeler ("MTW") call the "spin 2 derivation" and seem to believe it is somehow "inelegant" compared to the geometric derivation, but it appears equally valid and the resulting equations are the same. To make an analogy, quantum mechanics can be formulated either in the "Heisenberg picture" or the "Schrödinger picture", which make identical predictions but describe things differently. Neither is better than the other. In keeping with Wikipedia's NPOV policy, shouldn't we talk about both viewpoints? Einstein believed in the power of Occam's razor, but ironically Weinberg's approach actually has fewer axioms (i.e. the equivalence principle does not have to be put in ad hoc).

69.140.12.180 (talk) 14:54, 28 July 2009 (UTC)Nightvid

:Unfortunately, I have not read the paper to which you refer. However, I would like to make the following points: (1) Quantum mechanics and spinors are even harder to understand than classical GTR. (2) It is not enough that a theory leads to the correct result; it must also not lead to false results. I have heard that attempts to combine quantum mechanics and GTR always lead to inconsistencies, i.e. false results. (3) The equivalence principle is not some arbitrary add-on to GTR; it is the essence of what distinguishes the force of gravity from other forces, that is, it is the defining characteristic of gravity. (4) Using perturbation theory is like the derivation of GTR by developing an infinite sequence of tensor fields, beginning with the Minkowski metric and adding them together. This is certainly very inelegant compared to treating the metric as a single whole tensor. JRSpriggs (talk) 23:36, 29 July 2009 (UTC)

:NPOV doesn't mean giving equal importance to everything. Actually WP also has a policy of not giving *undue* weight to a particular person, point of view, or authority; since the geometric approach is the most commonly used approach, it makes sense to concentrate on it. And WP has a policy of making articles accessible to the general reader, whereas the kind of change you're talking about would have the effect of making this article less accessible than it already is. GR is a huge field. One article can't cover everything.--75.83.69.196 (talk) 06:11, 1 February 2010 (UTC)

A discussion of a [http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html relativistic rocket] accelerating past a line of evenly spaced stationary synchronized clocks would be an obvious way to explain the principles of general relativity without getting too technical. It only requires o good grasp of special relativity.

Since, from the point of view of the rocket, the clocks are becoming more and more out of sych, while at the same time the entire line is shrinking and moving past the rocket, there is a point behind the rocket where the clocks 'pile up' and time slows to a halt. A kind of 'black hole'. Lemmiwinks2 (talk) 22:38, 30 August 2009 (UTC)

Some have commented that the image :File:Black Hole Milkyway.jpg may not be accurate. Thoughts? Shawnc (talk) 21:49, 10 December 2009 (UTC)

:I've commented at that talk page (and split comments into proper threads). The only substantial complaint that I can see is that light near the hole should be dimmer (it's lensed to spread out over a larger solid angle), but I'm not sure that would make the image a better teaching tool. --Christopher Thomas (talk) 22:17, 10 December 2009 (UTC)

Some people from the /b/ forum have decided to vandalize this page, just a heads up.

-- ScaldingHotSoup ^(talk) 03:23, 20 January 2010 (UTC)

The illustration of the elevator principle is slightly misleading, as the rocket ship is shown leaning to the right. Really to be most accurate and easiest to understand, it should be exactly vertical, so that the ball falls in the same fashion as on the ground. In other words, if the rocket ship is leaning to the right, the ball will still fall according to gravity, so it will end up falling somewhere toward the rightmost side of the rocket-ship, or a straight line vertical drop regardless of the tilt of the rocket ship. In the illustration, it appears to suggest that the tilt of the rocket ship will alter the way the ball falls to the ground, which really is the opposite of what the article is conveying. I know it's a little nit-picky, but it would make the illustration a lot clearer. The basic principle is that gravity will have the same effect regardless of the velocity, tilt, or trajectory of the elevator. For instance (not the same example but a similar one), if a person is falling free fall in an elevator that has lost control and is falling to the ground, jumping up in the air at the last minute will not change the total impact of the fall. Similarly, if a rocket ship shoots up into the air, even if it turns or changes direction somehow, the force of gravity is still acting in the same direction. The center of gravity is still the earth and not the floor of the rocket ship. —Preceding unsigned comment added by Simplistic Linguist (talk • contribs) 18:02, 14 February 2010 (UTC)

:No, the picture is correct as it stands. The rocket falls in the ambient gravitational field which cancels out the first-order effects of any external field. However, the acceleration due to the rocket's propulsion creates an additional "gravitational field" inside the rocket which is directed to the rear of the rocket in the internal frame of reference. So the picture is right. JRSpriggs (talk) 07:55, 15 February 2010 (UTC)

I think it is weird that the article(and/or the theory of relativity) mentions the "curvature" of spacetime (space and time). Time is not curved. Time is an interval. Perhaps the better words would be "space and movement through space". —Preceding unsigned comment added by Jsolebello (talk • contribs) 16:27, 29 July 2010 (UTC)

:Spacetime is a manifold on which coordinate axes for space and time can be drawn (in any number of ways). What you are calling "time" is the distance between two points as measured along one such arbitrarily-defined axis. This is not related to whether the axis line, or the spacetime surface in which it's embedded, is curved. In practice, because the time axis chosen for coordinates is usually an inertial frame (at rest from at least one observer's point of view), it follows a geodesic, which could be considered "straight" depending on your definitions. That doesn't change the fact that the "surface" on which it's drawn (the manifold representing spacetime) is itself curved.

:I hope this answer is useful to you. --Christopher Thomas (talk) 18:15, 29 July 2010 (UTC)

::To Jsolebello: To see how naive your comment is, consider this analogy to the curvature of the surface of the Earth: << Latitude is not curved. Latitude is an interval. Perhaps the better words would be "longitude and movement through longitude". >>. JRSpriggs (talk) 22:08, 29 July 2010 (UTC)

Ok. I got it. Thanks for your help. It sounds like outer-space is wavy(like an ocean), and not simply curved. And, it depends on where you are. —Preceding unsigned comment added by 76.106.186.17 (talk • contribs) on 18:13, 2 August 2010

:Spacetime is curved (not just "wavy"). "Space" is a slice of this four-dimensional surface taken in an arbitrary direction (many valid directions exist, depending on what reference frame you choose to call "at rest"). For most of the universe, "space-like" slices look pretty flat. Gravitational waves could be thought of as moving ripples in space (or a stationary wake-like pattern in spacetime), but that doesn't seem to be what you were asking about. The gravity wells of planets, stars, and so forth don't make wave-like patterns, but instead make negative-curvature regions that don't have a really good visual analog.

:For more information, I suggest following one of the links listed at the top of this talk page. --Christopher Thomas (talk) 21:27, 2 August 2010 (UTC)

This article has two dead link, [http://toolserver.org/~dispenser/cgi-bin/webchecklinks.py?page=general_relativity see here]. Please update link. Earthandmoon (talk) 10:05, 28 August 2010 (UTC)

:Done. I've only fixed the ones that were flagged as broken, not the other problems flagged by that link. --Christopher Thomas (talk) 20:52, 28 August 2010 (UTC)

In considerations to Schwarzschild radius and spacetime curvature, it may indicate that the space near an atom is denser in energy near the atom. The electron going from a lesser energy orbit further form the nuclei, to a deeper orbit near the nuclei will cause the spacetime curvature near the nuclei to omit energy-pulse in the form of a photon, away form the nuclei in exchange for the volume of space near the nuclei that the electron will occupies closer to the nuclei in the newer orbit. Noteing, that photon, electron, and nuclei all have electric and magnetic filed and that electron and nuclei have mass's and in order to observe energy conservation at all levels. In other words, every point of space or so called "vacuum" has an energy value specific to the point location. A volume in space is to be replaced "suddenly" by mass will cause the space or "vacuum" to go certain geometrical energy distribution and conformational changes to accommodate that changes which is now occupied by mass. A conclusion my be deduced that space is homogeneous to its own and when forced to accommodate a change in its energy distribution as in the addition of a mass to point location in it, it undergo certain changes to maintain that equilibrium or to observe the new physical system in place equilibrium.--e:Y,?:G 19:23, 13 October 2010 (UTC) —Preceding unsigned comment added by E:Y,?:G (talk • contribs)

:Wikipedia is not a good place to propose your own new ideas about physical phenomena (per WP:NOR). All it can report is things that have been published already in appropriate sources (per WP:RS).

:The nuclei of atoms are far larger than their schwarzschild radius, so effects due to general relativity are minimal. Electrons circling these nuclei can have energies high enough that special relativity becomes relevant; this is already well-known and its effects are well-understood. --Christopher Thomas (talk) 20:57, 13 October 2010 (UTC)

Has Quantum fields theory in curved space time been confirmed by experimental or observed evidence ? by which evidences? 222.252.111.226 (talk) 06:59, 22 November 2010 (UTC)

:Not to the best of my knowledge. The only place to test it would be near the surface of a neutron star or near the event horizon of a black hole, as otherwise spacetime is close enough to flat for differences from flat spacetime predictions to be unmeasurably small.

:That said, there are about four different arguments from completely different approaches that predict Hawking radiation. The fact that a semiclassical approximation produces the same prediction is a point in its favour. The key word here is "approximation". "QFT in curved spacetime" is an approximate way of formulating QFT that doesn't require a complete theory of quantum gravity. The goal is to produce more accurate predictions than flat-spacetime QFT would in situations where "flat spacetime" is not a good approximation of reality. --Christopher Thomas (talk) 09:11, 22 November 2010 (UTC)

::So what are obstacles to against QFT in curved spacetime to become a complete theory of quantum gravity? Thanks you for your answer! 222.252.117.191 (talk) 02:55, 23 November 2010 (UTC)

:::The obstacle is that curved-spacetime QFT still has the structure of spacetime specified as a fixed, externally-imposed condition. Perturbations to it are allowed (gravity waves and so forth), but a full theory of quantum gravity could evolve arbitrarily changing geometry. GR can do this in a non-quantized manner, but trying to quantize these changes leads to difficulties (per the quantum gravity article). --Christopher Thomas (talk) 03:47, 23 November 2010 (UTC)

In the section where Einstein-Cartan Theory (EC) is mentioned, "Einstein's Equations", I added one paragraph that says that EC is proven to be a necessary extension of GR, in order to model spin and spin-orbit coupling correctly. For decades, EC was regarded as one of the haze of speculations surrounding GR, and a theory that requires additional assumptions beyond GR. The Wikipedia article on Einstein-Cartan Theory caused some controversy several years ago, and I credit the editors with getting expert outside review to resolve the matter. If anyone wants to remove this paragaph or substantially change its content, please check with the editor responsible for the article on EC, and I would like to be involved in the discussion. Thank you. Richard Petti (rjpetti@alum.mit.edu) Rjpetti (talk) 16:15, 26 November 2010 (UTC)

In the past two days, someone deleted my edit in the section "Einstein's equations" mentioning that Einstein-Cartan theory is a necessary extension of GR in order to model spin angular momentum correctly. Can the party responsible at least leave me a comment here or email me at rjpetti@alum.mit.edu so we can discuss this? The idea of taking such action without any recourse, identification or discussion is not the way to do this. Thank you. rjpetti Rjpetti (talk) 21:03, 28 November 2010 (UTC)

:Please show that it is impossible to model spin angular momentum without modifying the Einstein equations. In particular, without making them non-symmetric. Why can one not merely add terms to the expressions for the momenta of spinning particles which are the curl/divergence of an anti-symmetric tensor (the circulating momentum of the field), and then convert those momenta into symmetric stress-energy tensors in the usual manner? JRSpriggs (talk) 01:05, 29 November 2010 (UTC)

{{collapsetop|Off-topic per wp:talk page guidelines. This is the place where we discuss the article - not the subject.}}

General relativity was invented in order to get rid of the gravitational action at a distance, which was so abhorred by Einstein (he tried to ridicule nonlocality by devising the EPR paradox). By geometrizing the gravitational force, he effectively hid it like a spooky skeleton in a closet. As a result, the spatial frame of reference became crooked. It is impossible to describe objects in a reference frame which is wrinkled and crumpled. That is why the concept of crooked space needs to be scrapped in favour of Minkowski space. It does not even serve its original purpose—nonlocality has become universally accepted despite all Einstein's attempts to get rid of it. The "king" of modern science is not just naked. He is also dead, and it is time to bury his wrinkled and crooked corpse. 89.110.6.213 (talk) 06:54, 29 November 2010 (UTC)

:All attempts to make gravity consistent with pure special relativity have failed. If you keep trying to patch the theory to make it consistent with experiments and internally consistent, then you are led inexorably to general relativity. JRSpriggs (talk) 10:00, 29 November 2010 (UTC)

::If you keep patching the theory while simultaneously trying to preserve the principle of locality in its most primitive form, then you are indeed led inexorably to general relativity. Einstein was against any nonlocality because it implies irrational holism, which was at the basis of many Anti-semitic doctrines of that time. Now that the battle against nonlocality is lost, there is no need to cling to general relativity. In order to get rid of the wrinkledness and crumpledness of the spatial reference frame, we just need to stop geometrizing the gravitational force. Calculations in curved space are intractable due to their nonlinearity and are never performed in practice (everyone calculates using forces and flat space). That is why general relativity has always been a purely ideological construct of no practical value. 92.100.163.72 (talk) 16:50, 29 November 2010 (UTC)

:::The scientific validity of GR is not to be argued based on "ideology", Antisemitism or whether space is too "crumpled" for your taste or the calculations too difficult. Is it mathematically consistent as a classical theory? yes. Does it pass nontrivial experimental tests? yes. Has it ever been falsified by measurements? no. So what is your point? If you can devise an alternative model which makes the same successful experimental predictions including cosmology, go ahead. In the meantime your arguments are pointless. Aknochel (talk) —Preceding undated comment added 17:36, 29 November 2010 (UTC).

::::Both Gravitomagnetism and Minkowski space were formulated before general relativity. De facto, in any scientific and applied calculations proudly branded as "general-relativistic," mankind uses Gravitomagnetism plus Minkowski space. General relativity proper (Gravitomagnetism plus curved space) is never used in actual scientific or applied calculations. It is a nonexistent chimera. Since we do not use it, we should lose it. 92.100.163.72 (talk) 17:58, 29 November 2010 (UTC)

{{collapsebottom}}

This size of this article is currently at a little over 167,700 KB bytes. This could cause problems for some readers to download the aricle. In fact, tt is a slow download on my computer. Should we discuss spltting the article per WP:SPLIT and summary style WP:SS ? ---- Steve Quinn (talk) 20:37, 13 December 2010 (UTC)

:Article statistics (using: User:Dr pda/prosesize)

:*Article size (wikicode): 164 kB

:*Prose size: 50 kB

:*Total file size (including images): 514 kB.

:Most of the size of the page is due to images. Cutting down on text will do very little for the download speed of the page, unless we also cut down on the number of images. Or conversely, cutting down on images has much more effect than cutting down on text.TimothyRias (talk) 09:18, 14 December 2010 (UTC)

:About summary style. Most of the sections in the article are already in summary style, do you have any particular strategy in mind for cutting down the size?TimothyRias (talk) 09:21, 14 December 2010 (UTC)

::To TimothyRias: Good point. I commented out the image of the first page of Einstein's paper. It is not legible at this resolution and conveys no useful information (just an old piece of paper with handwriting on it). JRSpriggs (talk) 10:27, 14 December 2010 (UTC)

:::I have simplified some refs and reduced weasel that removed 10k of code and text. There should be much wording (weasel) to cut down. The reference list takes much of the article; I'm not sure they are all used. Materialscientist (talk) 11:36, 14 December 2010 (UTC)

::::I only opened this thread to start a discussion, and I had no strategy in mind. I was thinking that the regular editors of this article might have better solutions than I. However, if there is only 50 KB of prose, then maybe removing some images might be helpful. Also, Materialscientist has noted the reference list takes up much of the article, so maybe we could work on that. He also noted that cutting down on weasel wording would free up some Kilobytes - so maybe we could work on that. Looking at the reference section - it sure is extensive. Perhaps we could also get rid of some of the entries in the notes section. What do you guys think? ---- Steve Quinn (talk) 19:38, 14 December 2010 (UTC)

:::::Yes, the article is referenced up the wazoo, probably over-referenced even if they are all used. Because of the extensive inline citations, the Further reading and External links sections don't enhance the article. I favor [http://en.wikipedia.org/w/index.php?title=General_relativity_resources&action=history recreating this article] as a list, and moving those two sections there. It is currently a circular reference in the See also section. Tim Shuba (talk) 21:05, 14 December 2010 (UTC)

:::::*If it works, it sounds like a good idea to me. ---- Steve Quinn (talk)

The article contains many templates (190 notes linked to some 100+ refs, plus other stray templates in further reading, images, etc). This slows down loading too. One way to reduce length is to change citation style from Harvard (double link) to directly quoting refs in the text. This would also allow to shorten the author lists, but would clutter the main text code. The current author list (last1,2,.., first1,2,...) formatting takes much space and can't be changed to a simpler |author=X, Y, Z, because this would break the Harvard links. Materialscientist (talk) 06:00, 15 December 2010 (UTC)

: I agree. Changing the style of reference templates would probably help a lot. I am thinking of copying this article to one of my sub pages, and we can all work on it there. That way the main space article isn't in a state of flux while being worked on. And especially, there won't be two styles of reference templates (if that is what we decide to do). Also we will be able to edit more freely ( I suppose). Does this sound like a good idea? ---- Steve Quinn (talk) 06:57, 15 December 2010 (UTC)

:Also, because this is a feature article, it would probably be best not to work on it in the main space. It would be easier to recover from mistakes on a sub page. ---- Steve Quinn (talk) 07:00, 15 December 2010 (UTC)

::I would advise reaching consensus on which direction to go to. This would save much time (I've just wasted nearly 2 hours because of some referencing subtleties). I see two ways: (i) keep the material and compact the code (by abandoning the Harvard style) (ii) Cut or split but keep the current reference formatting. Perhaps some further reading can be cut without much problem, but this is not much. Materialscientist (talk) 07:06, 15 December 2010 (UTC)

:::To try stuff out we can actually use the talk:General relativity/WIP sandbox.

:::About changing the reference style. Is it clear that this would make a big performance difference?

:::One citation style I have useful is to use an hybrid Harvard style, where the first reference to a work is cited in the "normal" (non-harvard) footer style, and any subsequent reference to the same work uses a harvard style reference to the first mention of the work. This prevent having to use double links for sources that are only referenced once, but prevents sources that are cited multiple times with different page numbers being repeated.TimothyRias (talk) 17:26, 16 December 2010 (UTC)

::::I agree with recreating General relativity resources and moving most reference materials to it.

::::I disagree with having another version of the article whether in the sandbox here or under Steve Quinn's user page or elsewhere. I fear that changes will be made in the article which will not be reflected in the version under development. This will result in a great deal of wasted effort when the development version is used to overwrite the article, or discarded, or merged. Even if someone takes it upon himself to copy all good changes to the article into the development version, it will screw up the revision history of the article creating uncertainty as to who is responsible for a change. It is also likely that some material which is marginal will be effectively removed by not being added to the development version. This changes the presumption from retention to removal, contrary to Wikipedia's normal practices. JRSpriggs (talk) 21:37, 16 December 2010 (UTC)

There seems to be some disagreement among editors and sources about the year in which Albert Einstein (or David Hilbert) first published the correct form of the Einstein field equations for GR. According to our article List of scientific publications by Albert Einstein, it was Einstein's last paper of 1915:

::Schilpp 85; CP 6, 25 1915 Die Feldgleichungen der Gravitation

::The Field Equations of Gravitation

::Preussische Akademie der Wissenschaften, Sitzungsberichte, 1915 (part 2), 844–847 General relativity.[100] This is the defining paper of general relativity. At long last, Einstein had found workable field equations, which served as the basis for subsequent derivations.

Apparently, many other sources say that it was first published in 1916, perhaps referring to his second paper of 1916:

::Schilpp 89; CP 6, 30 1916 Grundlage der allgemeinen Relativitätstheorie

::The Foundation of the General Theory of Relativity

::Annalen der Physik (ser. 4), 49, 769–822, link General relativity.[102]

Which shall we use? See also History of general relativity and Relativity priority dispute. JRSpriggs (talk) 10:41, 26 February 2011 (UTC)

:1915 is correct, since Einstein's paper "Die Feldgleichungen der Gravitation" (which at last contained the correct field equations) was submitted November 25, and published December 2, 1915. The extended paper "Die Grundlage der allgemeinen Relativitätstheorie" (received March 20, 1916) was his first major review paper on this subject. --D.H (talk) 13:03, 26 February 2011 (UTC)

Hi. I'm not really an editor on here nor do I know much about physics past high school. I was wondering if this page should be edited to include new information that NASA's released about their [http://science.nasa.gov/science-news/science-at-nasa/2011/04may_epic/ Epic Space-Time experiment]. Maybe someone could make a new page about it or something? Just an idea. 124.168.140.62 (talk) 04:46, 13 May 2011 (UTC)

: There is a page about it. See Gravity Probe B. Roger (talk) 04:56, 13 May 2011 (UTC)

I see no mention of basic assumptions. It's my understanding, for example, that all bodies in GR are assumed to be point masses. Is this correct? If so, this would make singularities for Black Holes a trivial solution. Virgil H. Soule (talk) 18:16, 11 June 2011 (UTC)

:Not at all. Unlike the older equation

::$R\_\{\backslash mu\; \backslash nu\}\; =\; 0\; \backslash ,$

:which is only valid in a vacuum, the Einstein field equations contain the stress–energy tensor on one side and are valid everywhere. This allows one to calculate the metric inside a massive body such as a star. JRSpriggs (talk) 15:22, 12 June 2011 (UTC)

To {{user|Ancheta Wis}}: You added a 'reference' to the General relativity#History section which says "See course notes by John Archibald Wheeler (1962), Geometrodynamics, followed by a 1964 book by Wheeler & three of his students, followed by a 1966 book on Spacetime Physics, etc. Wheeler & Ford 1998, p. 253 stated "In earlier years [before 1956], I had feared that a student trained [to Ph.D. level] in general relativity might have trouble finding a job...".". This is not a single reliable secondary source. Rather it appears to me to be a violation of WP:SYN. Since you re-added it after I commented it out, I must ask you to justify why it is not a violation of policy or else revert yourself. JRSpriggs (talk) 09:58, 24 August 2011 (UTC)

(i)As I understand, according to The General Theory of Relativity, Geodesic is a 'straight' line in the "curved space-time"; and motion of the planets are inertial-motions along the geodesics. Now, while traveling in straight-line on the flat surface one can take a tea-break and then proceed further. Is it possible to take a tea-break while traveling along the geodesic, and then proceed further with the same or different speed? (ii) Inertial motion of an object can be at any speed; is it possible for the planets to travel at any speed along their orbits? Hasmukh K.Tank.123.201.22.165 (talk) 14:37, 6 September 2011 (UTC)

:(i)I understand taking a break as waiting some time in one given point in space.Here time is one of the coordinates of the space where the geodesic is being followed, so taking a break makes no sense since there isn't a second time coordinate with respect to which to take a break. (ii)Speed is defined as variation of space with respect to time but time here is one more coordinate of space so the inertial motion also fixes the speed. Now different geodesics will of course lead different speeds, but they will also lead to different trajectories so the planets would not be able to follow the same orbits at different speeds. Dauto (talk) 23:01, 6 September 2011 (UTC)

(ii) Inertial motion can be at any speed; whereas planets are compelled to travel at a specified speed predicted by Newtonian mechanics. I am not able to understand what Einstein wants to convey when he says: "Planetary orbits are just inertial-motion of planets in the 'curved space-time'. Moreover, can any one travel at any desired speed in time? Time always flows at its own speed, so time-axis is very much different from the space-axis; and so, in the so-called space-time-continuum, all axis are not equivalent. Hasmukh K. Tank123.201.22.176 (talk) 17:42, 7 October 2011 (UTC)

:Planets are not compelled to travel at only a specified speed. If a planet has an encounter with another celestial body, its speed will change and as a result the path it follows through space will change as well.

:In relativity, time is treated as a spatial dimension. So it is best to parameterize the trajectory of a particle with a fifth coordinate — it could be same as: the proper time, the time dimension in this or another coordinate system, a spatial dimension in some coordinate system, or some other convenient parameter. A point particle in free fall obeys the equation

::$\backslash frac\{d\; p\_\backslash mu\}\{d\; t\}\; =\; \backslash Gamma^\{\backslash lambda\}\_\{\backslash mu\; \backslash nu\}\; p\_\{\backslash lambda\}\; \backslash frac\{d\; x^\backslash nu\}\{dt\}\; \backslash ,$

:where $x^0\; \backslash ,$ is the time coordinate and $t\; \backslash ,$ is the parameter (fifth coordinate) chosen for this particle's trajectory, $\backslash Gamma^\{\backslash lambda\}\_\{\backslash mu\; \backslash nu\}\; \backslash ,$ is the Christoffel symbol (which is the gravitational force field), and $p\_\backslash mu\; \backslash ,$ is the linear momentum 4-vector given by

::$p\_\{\backslash alpha\}\; =\; m\; \backslash ,\; g\_\{\backslash alpha\; \backslash beta\}\; \backslash ,\; \backslash frac\{d\; x^\{\backslash beta\}\}\{d\; \backslash tau\}\; \backslash ,$

:where $m\; \backslash ,$ is the mass and $\backslash tau\; \backslash ,$ is the proper time measured along the particle's trajectory. JRSpriggs (talk) 20:21, 7 October 2011 (UTC)

Should a section, or note, be made regarding the faster than light neutrinos detected during the OPERA experiments and the potential implications they have in regards to General Relativity? — Preceding unsigned comment added by 216.123.241.196 (talk) 22:19, 20 November 2011 (UTC)

:No. (mostly because there are none.)TR 22:44, 20 November 2011 (UTC)

Would it be objectionable to separate footnotes that are discussion notes, from footnotes that are citation refs, using 'group='? (The current Notes section intersperses both, of course.) Why? (I hope no one asks that!) Cheers, Ihardlythinkso (talk) 02:28, 30 December 2011 (UTC)

Somehow the code:

< div style="position: fixed; top: 0px; left: 0px; z-index: 99">